Partner particles for moving mirror radiation and black hole evaporation
M. Hotta · R. Schützhold · W. G. Unruh
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In one page
Masahiro Hotta, Ralf Schützhold and William Unruh ask a sharp question about empty space. When a mirror accelerating through vacuum throws off a particle — the tabletop stand-in for Hawking radiation from a black hole — what is that particle entangled with? Quantum mechanics says it must have a partner, because such pairs are drawn out of the vacuum together. The three authors define the partner mode exactly, prove the definition fixes it uniquely, and then compute it: for a detector that is simply switched on and off, for an amplifier, and for the accelerated mirror. The answer is remarkable. The partner is itself nothing but a vacuum fluctuation, sitting in a region no local measurement can tell apart from empty space — not even a measurement of the energy density. Information and energy come apart. The correlations are really there, carried by something that registers as nothing, and the authors point out that this is the same accounting quantum energy teleportation runs on.
Why it matters hereChapter 2 argues that the vacuum is a structured medium rather than an absence, and this is one of the cleanest demonstrations of the point: a region that measures as empty can still be carrying the full correlations of a thermal emission. Chapter 13 needs exactly that bookkeeping, and chapter 6 inherits the authors’ own observation that those hidden correlations are what an energy-extraction protocol would draw on.
What it claims
01The partner mode of a given Hawking-type mode can be defined uniquely by two conditions — that the pair together be in a pure state once everything else is traced out, and that annihilating one partner particle leave the same state as creating one Hawking particle — and the appendix proves this fixes the partner completely, except when the Hawking mode is pure single-mode squeezing and needs no partner at all.Section II, definition of partner particle, with the uniqueness proof in Appendix A (arXiv:1503.06109v3)
Published and peer-reviewed02Partner particles are not a black-hole speciality. Any particle detection has one, including the excitation of a stationary Unruh-DeWitt detector produced by nothing more than switching the coupling on and off.Section III, Partners and detectors (arXiv:1503.06109v3)
Published and peer-reviewed03For the exponentially accelerated mirror — the standard toy model of black hole evaporation — the partner wave function comes out as approximately the mirror image of the Hawking mode on the far side of the horizon, squeezed into exponentially short wavelengths just past the horizon.Section VI, equations 90 and 91, and Figure 3 (arXiv:1503.06109v3)
Published and peer-reviewed04The headline result: the partner particles of the thermal radiation emitted by a mirror or a black hole are concentrated in a region that is locally indistinguishable from vacuum. No series of local measurements, energy density included, separates that region from empty space.Abstract, and Section VII Conclusions, opening paragraph (arXiv:1503.06109v3)
Published and peer-reviewed05Information therefore need not be carried by energy transport. The familiar argument that an evaporating black hole must release an enormous burst of energy at the end in order to carry out the information it holds does not follow: that information can leave in the form of vacuum, carrying none.Abstract and Section VII Conclusions (arXiv:1503.06109v3)
Published and peer-reviewed06The authors note that if the outcome of the Hawking-side measurement could be signalled to the partner region, energy could in principle be extracted from a state that is locally vacuum — the mechanism of quantum energy teleportation. In this geometry causality blocks the signal, because the two events are space-like separated.Section VI, paragraph following equation 91 (arXiv:1503.06109v3)
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https://doi.org/10.1103/PhysRevD.91.124060LICENCE. Published as Physical Review D volume 91, article 124060 (2015). Crossref lists only the APS default licence and both Unpaywall and the site’s own fetch record return closed with a null licence; no Creative Commons statement exists on the journal page, so no text of the published article is reproduced here. SOURCE READ. The authors’ own preprint, arXiv:1503.06109v3 dated 21 April 2015 and titled ‘On the partner particles for moving mirror radiation and black hole evaporation’, was downloaded and read in full for this page; it carries the arXiv non-exclusive distribution licence, which permits arXiv to distribute it but is not an open licence, so it too is summarised rather than reproduced. The locators below cite the preprint’s section numbers and equations, which run parallel to the published article. Author affiliations as printed: Masahiro Hotta, Graduate School of Science, Tohoku University; Ralf Schützhold, Fakultät für Physik, Universität Duisburg-Essen; William G. Unruh, Department of Physics, University of British Columbia and the CIAR Cosmology and Gravity Program. RELATED PAGES. The moving-mirror and dynamical-Casimir family on this site: ‘Fifty Years of the Dynamical Casimir Effect’ at /library/stm-984130a356, the Josephson-metamaterial measurement of that effect at /library/stm-c395407d90, the switched Unruh-DeWitt detector realised by electro-optic sampling at /library/stm-4144311706, the analogue-black-hole entanglement measurement at /library/stm-a3449e5f7e, and the Defense Intelligence Reference Document on quantum tomography of negative energy states in the vacuum at /library/stm-07d12a8c5d.
How to cite it
M. Hotta, R. Schützhold, W. G. Unruh (2015) Partner particles for moving mirror radiation and black hole evaporation. doi:10.1103/PhysRevD.91.124060
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